Miniature Fourier Transform Spectrometer Based on Thin-Film Lithium Niobate

A miniature Fourier transform spectrometer is proposed using a thin-film lithium niobate electro-optical modulator instead of the conventional modulator made by titanium diffusion in lithium niobate. The modulator was fabricated by a contact lithography process, and its voltage-length and optical waveguide loss were 2.26 V·cm and 1.01 dB/cm, respectively. Based on the wavelength dispersion of the half-wave voltage of the fabricated modulator, the emission spectrum of the input signal was retrieved by Fourier transform processing of the interferogram, and the analysis of the experimental data of monochromatic light shows that the proposed miniaturized FTS can effectively identify the input signal wavelength.


Introduction
Due to the ability to detect the characteristics of optical signals, spectrometers are widely used in many fields, such as space exploration [1], nanotechnology [2], bioengineering [3], modern medicine [4], meteorological monitoring [5], resource exploration [6], environmental monitoring [7] and life sciences [8]. With the development of science and technology, there is an increasingly urgent need for spectrometers to move from the traditional benchtop to miniaturization.
In recent years, the development of integrated optics has promoted the development of a miniature Fourier transform spectrometer (FTS) based on the electro-optical effect in lithium niobate (LN) to achieve a tunable optical pathlength difference (OPD) has received great attention.
In 1893, German physicist Pockels discovered the linear electro-optical effect, which revealed that the refractive index of certain crystals varies linearly with an applied voltage. As a material with a linear electro-optic effect, LN is a good material platform for miniature FTS because of its relatively large electro-optic coefficient, wide optical transparency window (0.4~5 µm), and low power consumption. In 2002, Howard constructed the first FTS based on bulk LN crystal [9]. Then a miniature FTS was introduced by Bentini et al. in 2007, which was achieved by utilizing high-energy ion implantation in LN [10]. In 2014, Li et al. proposed a miniature FTS, which is based on a conventional electro-optical modulator made by diffusing titanium into LN [11]. However, the electro-optical modulation efficiency of titanium diffused LN waveguide is low. Around 2016, thin film lithium 2 of 10 niobate (TFLN) wafers were commercially produced, giving rise to a series of studies based on TFLN [12][13][14][15][16]. TFLN waveguides are mostly formed by dry etching, allowing for high electro-optical modulation efficiency. There are many explorations of an electrooptical modulator based on TFLN, but there are few studies combining it with FTS. In 2019, Grange et al. combined the principles of LN electro-optical modulation and standing wave interference to propose a hybrid integrated FTS based on a TFLN-silicon nitride platform [17].
In this work, we present a miniature FTS based on a TFLN electro-optical modulator which was fabricated by a contact lithography process. Due to the half-wave voltage V π dependence on wavelength, the emission spectrum of the input signal is retrieved by the Fourier transform of the measured temporal interferogram. This work is of great value for the miniaturization of FTS.
This paper is organized as follows: Section 2 describes the detailed design of FTS and simulation of the modulator; then the fabrication, measurement, and analysis of results are presented in Section 3.

Design and Simulation
In this section, the general description of the device is given and then simulations are performed based on the relevant parameters to determine the dimensions of the modulation area.
The schematic diagram of the miniature FTS based on lithium niobate on insulator (LNOI) described in this paper is shown in Figure 1a, which consists of an electro-optical modulator, an arbitrary waveform generator (AWG), a photodetector (PD), a polarization controller (PC), a data acquisition card (DAQ), a signal processing unit, and input and output optical fibers. The core component is an electro-optical modulator based on LNOI, which consists of a Mach-Zehnder interferometer (MZI) and traveling wave electrodes (TWE), as shown in Figure 1b. Firstly, the optical signal is coupled into the MZI through the input fiber and propagates in the two arms of the MZI. At the same time, a modulating voltage is generated by the voltage generator and is applied to the TWEs on both sides of the waveguide, which leads to an opposite change in the refractive index of the two LN arms, thus modulating the OPD between both arms. Subsequently, the two optical signals interfere at the Y-branch combiner, and the interferometric optical signal is captured by the PD through the output fiber, and then is converted into an electrical signal at the output to the DAQ. Simultaneously, the modulating voltage is also sampled by the DAQ. Based on the Fourier transform principle and the relevant algorithms [18], the Fourier transform is performed on the acquired signals through the signal processing unit, and the emission spectrum of the input signal can be obtained. Among them, the V π of the electro-optical modulator has a great influence on the performances of the miniature FTS.
optical modulator based on TFLN, but there are few studies combining i 2019, Grange et al. combined the principles of LN electro-optical modulation wave interference to propose a hybrid integrated FTS based on a TFLNplatform [17].
In this work, we present a miniature FTS based on a TFLN electro-opti which was fabricated by a contact lithography process. Due to the half-wa dependence on wavelength, the emission spectrum of the input signal is re Fourier transform of the measured temporal interferogram. This work is of the miniaturization of FTS.
This paper is organized as follows: Section 2 describes the detailed des simulation of the modulator; then the fabrication, measurement, and ana are presented in Section 3.

Design and Simulation
In this section, the general description of the device is given and then s performed based on the relevant parameters to determine the dimensions o tion area.
The schematic diagram of the miniature FTS based on lithium niobat (LNOI) described in this paper is shown in Figure 1a, which consists of an modulator, an arbitrary waveform generator (AWG), a photodetector (PD), controller (PC), a data acquisition card (DAQ), a signal processing unit, a output optical fibers. The core component is an electro-optical modulator b which consists of a Mach-Zehnder interferometer (MZI) and traveling w (TWE), as shown in Figure 1b. Firstly, the optical signal is coupled into the the input fiber and propagates in the two arms of the MZI. At the same time voltage is generated by the voltage generator and is applied to the TWEs o the waveguide, which leads to an opposite change in the refractive index arms, thus modulating the OPD between both arms. Subsequently, the two interfere at the Y-branch combiner, and the interferometric optical signal the PD through the output fiber, and then is converted into an electrical sig put to the DAQ. Simultaneously, the modulating voltage is also sampled Based on the Fourier transform principle and the relevant algorithms [18 transform is performed on the acquired signals through the signal proces the emission spectrum of the input signal can be obtained. Among them electro-optical modulator has a great influence on the performances of the m The configuration and dimensions of the electro-optical modulator are shown in Figure 1b. The chip size is 7.5 mm × 0.25 mm, the modulating arm length of the interferometer is 5.5 mm, and the width of both waveguides is 1.1 µm. Considering that the input and output fiber waist diameters are 4 µm, the input port of the waveguide is designed with a tapered shape with the width gradually decreasing from 6 µm to 1.1 µm in order to make the input optical signal better coupled into the waveguide through the fiber, and the length of the taper is 500 µm. The output port of the waveguide is similarly designed. The two modulating arms are flanked by TWEs. Figure 2a shows the cross-sectional structure of the modulated region. From top to bottom, are the SiO 2 cladding layer, the two gold electrodes, the x-cut LNOI ridge waveguide, the SiO 2 buried layer, and the silicon substrate. The optical signals are confined in the ridge waveguide for transmission, and the sidewall roughness of the ridge waveguide is greatly affected by fabrication conditions. Considering that contact lithography is used in this research, in the simulations, the upper width of the ridge waveguide is set to 1.1 µm. When the modulating voltage is applied to the gold electrodes on both sides of the ridge waveguide, it will result in a change in the refractive index of the ridge waveguide. The electric field applied to the two arms of the interferometer in opposite directions causes opposite changes in the refractive index of the two arms, resulting in the OPD at the end of the interferometer. For the electro-optical modulator, the V π and optical waveguide loss are greatly influenced by the gap D of the two gold electrodes, the etching depth h of the ridge waveguide, and the height of gold electrodes H, as shown in Figure 2a. Related studies have shown [19] that the larger the gap D and the larger the etching depth h, the larger the V π and the smaller the optical loss caused by metal absorption. In order to obtain a relatively low V π and relatively small optical waveguide loss, with reference to the results of the literature [19] and a series of related simulations using COMSOL Multiphysics, in our research, the gap D is set as 5 µm, the etching depth h equals 300 nm and the height of gold electrodes H equals 900 nm. a tapered shape with the width gradually decreasing from 6 µm make the input optical signal better coupled into the waveguid the length of the taper is 500 µm. The output port of the wavegui The two modulating arms are flanked by TWEs. Figure 2a shows the cross-sectional structure of the modula bottom, are the SiO2 cladding layer, the two gold electrodes, the guide, the SiO2 buried layer, and the silicon substrate. The optica the ridge waveguide for transmission, and the sidewall roughnes is greatly affected by fabrication conditions. Considering that con in this research, in the simulations, the upper width of the ridge µm. When the modulating voltage is applied to the gold electro ridge waveguide, it will result in a change in the refractive index The electric field applied to the two arms of the interferomete causes opposite changes in the refractive index of the two arms, the end of the interferometer. For the electro-optical modulator, t guide loss are greatly influenced by the gap D of the two gold elect h of the ridge waveguide, and the height of gold electrodes H, Related studies have shown [19] that the larger the gap D and the h, the larger the Vπ and the smaller the optical loss caused by m to obtain a relatively low Vπ and relatively small optical wavegu to the results of the literature [19] and a series of related simulatio tiphysics, in our research, the gap D is set as 5 µm, the etching de the height of gold electrodes H equals 900 nm.  Based on the determined dimensions, the simulations were carried out by COMSOL Multiphysics, and the results are shown in Figure 2b,c, including the optical field of the simulated transverse electric (TE) mode and the electrostatic field of the gold electrodes, with a calculated electro-optic overlap integral factor of 0.5401. Then the V π and optical waveguide loss of the electro-optical modulator can be calculated based on COMSOL simulations. At λ = 1550 nm, the corresponding V π is 4.08 V, and the optical waveguide loss is 0.38 dB/cm.

Fabrication and Measurement of the Device
We use contact lithography to prepare the electro-optic modulator chip, and the fabrication process is shown in Figure 3. First, an 80 nm thick Chromium layer (Cr) is sputtered on the top surface of the exposed LNOI by magnetron sputtering, which is used as a hard mask for the etching process. A 1.2-µm-thick negative photoresist (PR) is then used to define the waveguide pattern. Next, the patterns are transferred into a Cr layer using an inductively coupled plasma (ICP) etcher, and subsequently into the TFLN by an optimized dry ICP etching process based on Ar and SF 6 . The physical and chemical reactions are carried out simultaneously during the TFLN etching process, and the etching speed is 0.32 nm/s. Then the residual Cr mask is removed using cerium ammonium nitrate. The metal electrode (15 nm-thick Cr/900 nm-thick Au) is then fabricated and formed by a standard lift-off process. A 1 µm thick silica cladding is then deposited by plasma enhanced chemical vapor deposition (PECVD). Then windows are made in the silica cladding to facilitate the connection of the bottom electrode to the top electrode afterward, and finally, a second lift-off process is performed to produce the top electrode.

Fabrication and Measurement of the Device
We use contact lithography to prepare the electro-optic modulat rication process is shown in Figure 3. First, an 80 nm thick Chromium tered on the top surface of the exposed LNOI by magnetron sputterin a hard mask for the etching process. A 1.2-µm-thick negative photores to define the waveguide pattern. Next, the patterns are transferred i an inductively coupled plasma (ICP) etcher, and subsequently into th mized dry ICP etching process based on Ar and SF6. The physical and are carried out simultaneously during the TFLN etching process, and 0.32 nm/s. Then the residual Cr mask is removed using cerium amm metal electrode (15 nm-thick Cr/900 nm-thick Au) is then fabricate standard lift-off process. A 1 µm thick silica cladding is then depo hanced chemical vapor deposition (PECVD). Then windows are mad ding to facilitate the connection of the bottom electrode to the top e and finally, a second lift-off process is performed to produce the top e   thick negative PR is used to define the waveguide pattern. (c) The patterns are then transferred into the Cr layer using ICP etcher, and (d) subsequently into the LN thin film using Ar and SF6. (e The residue mask materials are removed in cerium ammonium nitrate. (f) Bottom metal electrodes (15 nm-thick Cr/900 nm-thick Au) are formed using a standard lift-off process. (g) A 1 µm thick silica cladding layer is then deposited by PECVD. (h) Via windows are opened by wet etching. (i) A second lift-off process is performed to produce the top electrodes. Figure 4 shows the microscope image of a part of the fabricated modulator and th scanning electron microscope (SEM) image of a cross section of the waveguide. The uppe width of the ridge waveguide is measured to be about 1.1 µm, the sloping sidewall of th waveguide is about 75° from horizontal, and the bottom width of the ridge waveguide i about 1.2 µm. The measurement setup is shown in Figure 5. The input optical signal is generated by a tunable laser and coupled into the electro-optical modulator through the input fiber and PC. After modulation by the modulating voltage, the optical signals in the two arms interfere at the Y-branch combiner, and the interfering optical signals are captured by the PD through the output fiber and then are converted into electrical signals, and the DAQ is set at the end to capture the electrical signals. Table 1 compares the fabricated TFLN modulator in this work with the one obtained in the [19]. They have similar structures and working principles.  The measurement setup is shown in Figure 5. The input optical by a tunable laser and coupled into the electro-optical modulator thr and PC. After modulation by the modulating voltage, the optical sign interfere at the Y-branch combiner, and the interfering optical signals PD through the output fiber and then are converted into electrical si is set at the end to capture the electrical signals. Table 1 compares t modulator in this work with the one obtained in the [19]. They have si working principles.

Analysis of Measurement Results
In this section, the principle of optical signal identification based on FTS is described, and then the identification of the input optical signal based on the experimental data is conducted.
The change of OPD in the proposed miniature FTS is achieved by the electro-optical effect in LN. The opposite refractive index change caused by the modulating voltage V(t) will produce OPD although the physical paths of the two arms are the same. The OPD between the two arms can be expressed as where D is the gap between the two gold electrodes, L is the arm length, n e (λ), γ 33 (λ), Γ(λ) are the parameters related to modulator configuration and optical signal wavelength λ.
The half-wave voltage V π (λ) of the electro-optical modulator can be expressed as Substituting Equation (2) into Equation (1), we can get Defining g(λ) = 1/(2V π (λ)), Equation (3) can be rewritten as For a fabricated electro-optical modulator, L and D are all constant, and the parameters n e (λ), γ 33 (λ) and Γ(λ) have definite values when the input optical signal wavelength λ is determined. Then according to Equation (2), V π (λ), and g(λ) can be determined, and OPD is only related to the applied modulating voltage V(t) according to Equation (1).
The modulating voltage will cause the change of OPD, thus causing the change of the interferometric light intensity I. I varies with the modulating voltage V and can be expressed as follows, according to the FTS theory [11], where A(λ) is the light intensity in the emission spectrum of the input signal. Equations (4) and (5) can be rewritten as To facilitate the Fourier transform, Equation (6) is rewritten as [11] Micromachines 2023, 14, 458 7 of 10 Fourier transform of Equation (7) gives It is worth noting that due to the presence of a breakdown electric field (~10 V/µm) in LN, the range of modulating voltage is limited, then Equation (8) can be rewritten as where V max is the maximum modulating voltage, and A 0 (g) is the spectral intensity distribution with g. Since the collected data of the modulating voltage V(t) and the interferometric light intensity I are discrete sequences, the discrete Fourier transform is used, which is expressed as [20] A 0 (g) = A 0 (g) can be obtained through the discrete Fourier transform. Obtaining A(λ) from A 0 (g) also requires determining the dispersion relation between the half-wave voltage V π (λ) and the wavelength λ.
For the fabricated FTS, the dependence of V π on wavelength λ can be determined by experimentally measuring a series of input optical signals of different λ, and the study shows that the function has monotonicity [20]. By using the measured dispersion of V π (λ) and the formula g = [2V π (λ)] − 1, the plot of A 0 (g) against g can be converted into the wanted laser power spectrum A(λ). A more detailed discussion of the above theory can be found in the literature [11]. Based on the above principles, specific signal processing algorithms are written to analyze the experimental data of the fabricated miniature FTS, then the identification of the input optical signal can be conducted.
In order to obtain the half-wave voltage V π (λ) as a function of wavelength λ, a series of optical signals with different wavelengths (1528.8 nm, 1535.8 nm, 1545.3 nm, 1553.3 nm, 1566.7 nm) are fed in the TFLN electro-optic modulator, and the V π corresponding to a certain wavelength can be obtained by the intensity-versus-voltage interferogram, then a series of the values of V π and λ can be obtained, as shown by the black dots in Figure 6. The half-wave voltage dispersion can be obtained by fitting the measured multiple wavelengths to the half-wave voltage data, as shown in Figure 6. The fitting function is expressed as V π (λ) = 0.00853 × λ − 8.80257 (11) In order to verify the spectral detection capability of the miniature FTS proposed in this paper, the light signal with a wavelength of 1561.828 nm was fed into the miniature FTS as the light source to be measured, and the intensity-versus-voltage interferogram was obtained, as shown in Figure 7a. It can be read from Figure 7a that the half-wave voltage is 4.51 V, corresponding to a voltage-length product of 2.26 V·cm. After Fourier transforming of the interferogram, the plot of normalized A 0 (g) against g was obtained (as shown in Figure 7b), on which the plot of A(λ) against λ can be obtained utilizing the formula g = [2V π (λ)] − 1 and the Equation (11). It can be deduced that the main peak is located at 1561.46 nm, which is very close to the wavelength of the signal to be measured (1561.828 nm), indicating that the proposed miniature FTS can accurately identify the wavelength of the input signal.
shown in Figure 7b), on which the plot of A(λ) against λ can b formula g = [2Vπ(λ)] − 1 and the Equation (11). It can be deduce located at 1561.46 nm, which is very close to the wavelength of th (1561.828 nm), indicating that the proposed miniature FTS can wavelength of the input signal.  formula g = [2Vπ(λ)] − 1 and the Equation (11). It can be deduced that the main pea located at 1561.46 nm, which is very close to the wavelength of the signal to be measu (1561.828 nm), indicating that the proposed miniature FTS can accurately identify wavelength of the input signal.

Conclusions
A miniature FTS is proposed using a shallowly etched TFLN electro-optical modulator instead of the conventional modulator made by titanium diffusion in LN. The modulator was fabricated by a contact lithography process and ICP dry etching process, which can reduce the cost of the device. Its voltage-length product and optical waveguide loss were 2.26 V·cm and 1.01 dB/cm, respectively, and the measured results agree well with simulated results, which indicates that the simulation is a good guide to improve the modulator performance. The half-wave voltage as a function of wavelength was experimentally determined. Based on the wavelength dispersion of half-wave voltage, the emission spectrum of the input signal was retrieved by Fourier transform processing of the interferogram. A signal with a wavelength of 1561.828 nm was input to the proposed miniaturized FTS, and the signal spectrum with a peak located at 1561.46 nm was obtained with the help of the half-wave voltage dispersion equation and Fourier transform. This shows that the proposed miniaturized FTS can effectively identify the input signal wavelength. We believe that the miniaturized FTS presented in this paper can be a promising candidate for compact FTS.

Conflicts of Interest:
The authors declare no conflict of interest.